/* ----------------------------------------------------------------------
 * Project:      CMSIS DSP Library
 * Title:        arm_sqrt_q31.c
 * Description:  Q31 square root function
 *
 * $Date:        18. March 2019
 * $Revision:    V1.6.0
 *
 * Target Processor: Cortex-M cores
 * -------------------------------------------------------------------- */
/*
 * Copyright (C) 2010-2019 ARM Limited or its affiliates. All rights reserved.
 *
 * SPDX-License-Identifier: Apache-2.0
 *
 * Licensed under the Apache License, Version 2.0 (the License); you may
 * not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 * www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an AS IS BASIS, WITHOUT
 * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

#include "arm_math.h"
#include "arm_common_tables.h"

/**
  @ingroup groupFastMath
 */

/**
  @addtogroup SQRT
  @{
 */

/**
  @brief         Q31 square root function.
  @param[in]     in    input value.  The range of the input value is [0 +1) or 0x00000000 to 0x7FFFFFFF
  @param[out]    pOut  points to square root of input value
  @return        execution status
                   - \ref ARM_MATH_SUCCESS        : input value is positive
                   - \ref ARM_MATH_ARGUMENT_ERROR : input value is negative; *pOut is set to 0
 */

arm_status arm_sqrt_q31(
	q31_t in,
	q31_t *pOut)
{
	q31_t bits_val1;
	q31_t number, temp1, var1, signBits1, half;
	float32_t temp_float1;
	union {
		q31_t fracval;
		float32_t floatval;
	} tempconv;

	number = in;

	/* If the input is a positive number then compute the signBits. */
	if (number > 0) {
		signBits1 = __CLZ(number) - 1;

		/* Shift by the number of signBits1 */
		if ((signBits1 % 2) == 0) {
			number = number << signBits1;
		} else {
			number = number << (signBits1 - 1);
		}

		/* Calculate half value of the number */
		half = number >> 1;
		/* Store the number for later use */
		temp1 = number;

		/* Convert to float */
		temp_float1 = number * 4.6566128731e-010f;
		/* Store as integer */
		tempconv.floatval = temp_float1;
		bits_val1 = tempconv.fracval;
		/* Subtract the shifted value from the magic number to give intial guess */
		bits_val1 = 0x5f3759df - (bits_val1 >> 1);  /* gives initial guess */
		/* Store as float */
		tempconv.fracval = bits_val1;
		temp_float1 = tempconv.floatval;
		/* Convert to integer format */
		var1 = (q31_t)(temp_float1 * 1073741824);

		/* 1st iteration */
		var1 = ((q31_t)((q63_t) var1 * (0x30000000 -
										((q31_t)
										 ((((q31_t)
											(((q63_t) var1 * var1) >> 31)) *
										   (q63_t) half) >> 31))) >> 31)) << 2;
		/* 2nd iteration */
		var1 = ((q31_t)((q63_t) var1 * (0x30000000 -
										((q31_t)
										 ((((q31_t)
											(((q63_t) var1 * var1) >> 31)) *
										   (q63_t) half) >> 31))) >> 31)) << 2;
		/* 3rd iteration */
		var1 = ((q31_t)((q63_t) var1 * (0x30000000 -
										((q31_t)
										 ((((q31_t)
											(((q63_t) var1 * var1) >> 31)) *
										   (q63_t) half) >> 31))) >> 31)) << 2;

		/* Multiply the inverse square root with the original value */
		var1 = ((q31_t)(((q63_t) temp1 * var1) >> 31)) << 1;

		/* Shift the output down accordingly */
		if ((signBits1 % 2) == 0) {
			var1 = var1 >> (signBits1 / 2);
		} else {
			var1 = var1 >> ((signBits1 - 1) / 2);
		}
		*pOut = var1;

		return (ARM_MATH_SUCCESS);
	}
	/* If the number is a negative number then store zero as its square root value */
	else {
		*pOut = 0;

		return (ARM_MATH_ARGUMENT_ERROR);
	}
}

/**
  @} end of SQRT group
 */
